1. Field of the Invention
This invention relates broadly to methods and apparatus for investigating subsurface earth formations. More particularly, this invention relates to acoustic borehole tools and methods for measuring a characteristic of an earth formation. The invention has particular application to the measurement of formation nonlinearity.
2. State of the Art
The art of acoustic well logging for use in determining formation parameters is a well established art. Acoustic well logging generally encompasses both sonic and ultrasonic well logging. Sonic well logs are typically derived from sonic tools suspended in a mud-filled borehole by a cable. The tools typically include a sonic source (transmitter) and a plurality of receivers which are spaced apart by several inches or feet. Typically, a sonic signal is transmitted from the transmitter at one longitudinal end of the tool and received by the receivers at the other, and measurements are made every few inches as the tool is drawn up the borehole. The sonic signal from the transmitter or source enters the formation adjacent the borehole, and the arrival times of the compressional (P-wave), shear (S-wave) and Stoneley (tube) waves are detected by the receivers. The receiver responses are typically processed in order to provide a time to depth conversion capability for seismic studies as well as for providing the determinations of formations parameters such as porosity.
While measurements of the compressional, shear, and tube waves are useful in quantifying various parameters of the formation, it will be appreciated that to date, there has been no successful mechanism for making in situ determinations of nonlinear aspects of the formation. For purposes of this invention, it should be understood that the term "nonlinear" when used to describe a material relates to the fact that a plot of stress versus strain in a material will exhibit some nonlinear behavior. The more nonlinear the stress versus strain plot is, the more nonlinear the material is said to be. Various manifestations of nonlinearity include: the varying of the acoustic velocity in the material when the confining pressure changes; the varying of the acoustic velocity in the material when the amplitude of the acoustic wave changes; the interaction of two monochromatic acoustic beams having different frequencies to create third and fourth acoustic beams having the difference frequency and the additive frequency of the two incident beams; and evidence of frequencies being generated within the material which were not part of any input signal.
In the oil production industry, rock phenomena such as sanding, fracturing and borehole collapse can be considered to relate to the nonlinear properties of the formation. In each case, the strain in the rock catastrophically exceeds that which would be expected from a linear stress-strain relationship. As suggested in one of the parent applications hereto, since the less consolidated a formation is, the more nonlinear it is, a measurement of the nonlinearity of the formation can provide a measurement of the relative state of the consolidation of the formation. As suggested above, whether a layer of a formation is well or poorly consolidated, can broadly affect the producibility of the layer and formation, as well as the manner in Which production is to be carried out.